Many climate models have dry biases in the tropical monsoon regions, but it is less clear how these errors have affected the model-simulated tropical-extratropical interactions and rainfall teleconnections. In this study, we evaluate the Australia and Asian (A-A) monsoon rainfall in two versions (Global Atmosphere component GA 6 and GA7) of the UK Met Office Unified Model (UM) with AMIP-type simulations using two horizontal resolutions (N96 ~135 km and N216 ~60 km). Although the UM can capture broad features of rainfall seasonal variations in the A-A monsoon region, there are significant model errors in the locations of heavy monsoon rainfall, its magnitudes and time evolutions, and especially a climatological rainfall dry bias over the Indian subcontinent. This dry bias is progressively reduced with increased model resolutions from N96 to N216 and improved model physics from GA6 to GA7. Area-averaged peak monsoon rainfall over the Indian subcontinent (70-90^oE, 5-25^oN) increases by ~70% from 3mm day^-1 in GA6N216 to 5 mm day^-1 in GA7N216. Although GA7N216 still suffers a dry bias in the Indian monsoon region, the increased monsoon rainfall and the doubled atmospheric diabatic heating in the middle-upper troposphere lead to more realistic extratropical circulation Gill-type responses to the monsoon-induced diabatic heating. This results in improved monsoon-desert rainfall teleconnections, more realistic linkage between the tropical Asian monsoon with its subtropical East Asian component, and its interhemispheric influence in the Southern Hemisphere. Our study clearly demonstrates that uncertainty associated with model monsoon simulations needs to be considered in future climate projections even outside the monsoon domain.